false_of_nontrivial_of_product_domain

theorem false_of_nontrivial_of_product_domain : ∀ (R : Type u_9) (S : Type u_10) [inst : Ring R] [inst_1 : Ring S] [inst : IsDomain (R × S)] [inst : Nontrivial R] [inst : Nontrivial S], False

This theorem states that the product of two nontrivial rings cannot form a domain. In other words, if we have two nontrivial rings R and S, it is impossible to construct a domain from their Cartesian product R × S. This is a contradiction in terms, hence the result is `False`.

More concisely: The Cartesian product of two nontrivial rings cannot be a domain.